The conceptual and practical limitations of classical multiple linear regression models can be resolved naturally in a Bayesian framework. Unless based on an overly simplistic parameterization, however, exact inference in Bayesian regression models is analytically intractable. This problem can be overcome using methods for approximate inference.

This MATLAB toolbox implements variational inference for a fully Bayesian multiple linear regression model, including Bayesian model selection and prediction of unseen data points on the basis of the posterior predictive density.